Method for Determining a Residual Frequency Offset, Communication System, Method for Transmitting a Message, Transmitter, Method for Processing a Message and Receiver

ABSTRACT

A method of determining a residual frequency offset between a transmitter and a receiver in a transmission of data via a communication channel, is described, wherein the message is transmitted from the transmitter to the receiver via the communication channel and the message comprises at least one short preamble ( 201 ), at least one long preamble ( 202 ) and user data ( 203 ). The at least one long preamble ( 202 ) comprises residual frequency offset determination information based on which the residual frequency offset is determined.

FIELD OF THE INVENTION

The invention relates to a method for determining a residual frequencyoffset, a communication system, a method for transmitting a message, atransmitter, a method for processing a message and a receiver.

BACKGROUND OF THE INVENTION

In a SISO (single input single output) OFDM (orthogonal frequencydivision multiplexing) system, i.e. a communication system with onetransmit antenna and one receiver antenna which uses modulation of aplurality of subcarriers according to OFDM for data transmission,preambles are sent before the user data is sent for various reasons.First, short preambles are sent for timing synchronisation and frequencysynchronisation, in particular for frequency offset estimation.

Frequency offset estimation is necessary since in practical datacommunication, it cannot be expected that the local oscillator frequencyat the receiver is identical to that of the signal carrier generated atthe transmitter. This is for one due to circuit limitation and itparticularly arises if the receiver is in relative motion to thetransmitter as Doppler shift is inevitably introduced to the carrierfrequency.

A frequency offset may lead to inter-carrier interference (ICI). For amulticarrier system, such as one that adopts OFDM, a residual frequencyoffset results in a significant performance degradation.

After the short preambles, relatively few long preambles are sent in aSISO OFDM system (two in case of a system according to the IEEE802.11astandard, see [1]) which are employed for channel estimation. Since onlya single channel is established, few long preambles are enough forchannel estimation.

In case of a MIMO (Multiple Input Multiple Output) system where aplurality of transmit antennas are used, however, a higher number oflong preambles is necessary in order for all channel information to beextracted since a plurality of physical channels are employed fortransmission. In fact, it can be shown that in case of a MIMO system,the number of long preambles should be no less than the number oftransmit antennas.

Such an increase of the number of long preambles compared to a SISOsystem has the consequence that the time for transmission of the longpreambles, also called the long preamble duration, is increased comparedto a SISO system. This gives rise to a more substantial rotation of thephase in the data symbols succeeding the long preambles in the presenceof a residual frequency offset which is involuntary due to the finitenumber of short preambles for frequency offset estimation (FOE) in apractical communication system.

Due to the severity of the distortion, the data symbols sent first cantypically not be adequately corrected and error bits and error packetsare caused.

In [2] an estimator for frequency estimation is described.

An object of the invention is to provide a method for improved residualfrequency offset estimation in communication systems.

The object is achieved by a method for determining a residual frequencyoffset, a communication system, a method for transmitting a message by atransmitter, a transmitter, a method for processing a message and areceiver with the features according to the independent claims.

SUMMARY OF THE INVENTION

A method for determining a residual frequency offset between atransmitter and a receiver in a transmission of data via a communicationchannel is provided, wherein a message is transmitted from thetransmitter to the receiver via the communication channel. The messagecomprises at least one short preamble, at least one long preamble anduser data and the at least one long preamble comprises residualfrequency offset determination information. The residual frequencyoffset is determined based on the residual frequency offsetdetermination information.

Further, a method for transmitting a message by a transmitter isprovided, wherein a message is generated wherein the message comprisesat least one short preamble, at least one long preamble and user dataand the at least one long preamble comprises residual frequency offsetdetermination information and the message is transmitted to a receivervia a communication channel. The residual frequency offset determinationinformation allows the receiver to determine a residual frequency offsetbetween the transmitter and the receiver in the transmission of data viathe communication channel.

Further, a method for processing a message by a receiver is providedwherein a message is received from a transmitter via a communicationchannel which message comprises at least one short preamble, at leastone long preamble and user data, wherein the at least one long preamblecomprises residual frequency offset determination information. Aresidual frequency offset between the transmitter and the receiver in atransmission of data via the communication channel is determined basedon the residual frequency offset determination information.

Further, a communication system, a transmitter and a receiver accordingto the method for determining a residual frequency offset, the methodfor transmitting a message and the method for processing a messagedescribed above are provided.

SHORT DESCRIPTION OF THE FIGURES

FIG. 1 shows a communication system according to an embodiment of theinvention.

FIG. 2 shows a transmission block according to an embodiment of theinvention.

DETAILED DESCRIPTION

Illustratively, the long preambles are used for residual offsetestimation. In this way, even when a lot of long preambles aretransmitted, as it is the case in case of a MIMO (multiple inputmultiple output) system, since relatively many long preambles arenecessary for channel estimation, the residual frequency offset can beestimated and compensated without data loss.

The invention is for example applicable to communication systemsaccording to WLAN 11n, i.e. for wireless local area networks, but mayalso be applicable to large area communication systems such as mobiletelephone communication systems.

Embodiments of the invention emerge from the dependent claims. Theembodiments which are described in the context of the method fordetermining a residual frequency offset are analogously valid for thecommunication system, the method for transmitting a message, thetransmitter, the method for processing a message and the receiver.

In one embodiment, at least one short preamble comprises frequencyoffset determination information and a frequency offset is determinedbased on the frequency offset determination information.

The data can comprise further residual frequency offset determinationinformation and a residual frequency offset determination can be carriedout based on the further residual frequency offset determinationinformation.

In one embodiment, the communication channel comprises at least one datasubchannel and at least one pilot subchannel.

The at least one long preamble may further comprise channel estimationinformation based on which a channel estimation is performed todetermine the transmission characteristics of the communication channeland the frequency offset determination information may be transmittedvia the least one pilot subchannel and the channel estimationinformation may be transmitted via the at least one data subchannel.

This means that the pilot subchannels are used in the period of longpreamble transmission to transmit special symbols (i.e. pilot symbols),that allow the receiver to perform a residual frequency offsetestimation.

In one embodiment the message is transmitted via a plurality of transmitantennas. The message may be received via a plurality of receiveantennas.

The message is for example transmitted according to OFDM.

In one embodiment, when the residual frequency offset has beendetermined based on the residual frequency offset determinationinformation, a phase compensation is carried out for at least one signalvalue which is received in the transmission of the message based on thedetermined residual frequency offset.

For example, at one moment in time based on the frequency offsetdetermination information transmitted so far, a residual frequencyoffset determination may be carried out and all signal values receivedin the following are corrected (i.e. phase compensated) based on thedetermined frequency offset. When successively more residual frequencyoffset determination information is received in the course of time, theresidual frequency offset may be determined again to improve the currentestimate of the residual frequency offset.

In the embodiment described below, special pilots embedded in both longpreambles and data are described. A recursive estimation algorithm basedon the linear prediction method in [2] is described and a compensationformula that counteracts the effect on both the channel estimate and thedata is given.

Illustrative embodiments of the invention are explained below withreference to the drawings.

FIG. 1 shows a communication system 100 according to an embodiment ofthe invention.

The communication system 100 comprises a transmitter 101 (only partlyshown in FIG. 1) and a receiver 102.

The transmitter 101 comprises a plurality of transmit antennas 103,wherein each transmit antenna 103 is used for signal transmission. Data(user data, preambles, etc.) to be sent by a transmit antenna 103 inform of a radio signal is supplied to the transmit antenna 103 by arespective IFFT (inverse fast Fourier transform) unit 104. Radio signalstransmitted by the transmitter 101 are received by the receiver 102 viaa plurality of receiver antennas 105.

Modulation of subcarriers according to OFDM (orthogonal frequencydivision multiplexing) is used for the transmission of signal valuesform the transmit antennas 103 to the receiver antennas 105.

As the local oscillator in the receiver 102 cannot be guaranteed tooperate at exactly the same frequency as the one in the transmitter 101due to relative motion or imperfection in hardware circuitries, thedisparity gives rise to a frequency offset which rotates the receivedsignals by an angle that grows with time.

Therefore, short preambles are sent prior to user data. This isillustrated in FIG. 2.

FIG. 2 shows a transmission block 200 according to an embodiment of theinvention.

The transmission block 200 is sent from the left to the right, i.e. theelements of the transmission block 200 farthest to the left are sentfirst.

The transmission block 200 comprises short preambles 201 that are sentfirst and which are used for frequency offset estimation (FOE) by a FOEunit 106 of the receiver 102 after reception of the short preambles. TheFOE unit 106 estimates the frequency offset, in FIG. 1 denoted by ψ. Afrequency offset compensation unit 107 receives the frequency offsetestimate ψ as input and compensates the frequency offset for all furtherreceived signal values.

After frequency offset compensation, there remains a residual frequencyoffset, although usually a small quantity, in the form of inter-carrierinterference that destroys the orthogonality among the frequencysubchannels and could thus—if not compensated for—cause total systemfailure.

In the IEEE802.11a standard, frequency subchannels of indices[8,22,44,58] (with reference to the convention from 1 to 64) arededicated for pilot transmission in a SISO (single input single output)system with 64 frequency subcarriers. It is assumed that thecommunication system 100 is a MIMO (multiple input multiple output)system with N_(t) transmit antennas 103 and N_(r) receive antennas 105.The same frequency subchannels as in the IEEE802.11a standard, i.e. thefrequency subchannels of the indices [8,22,44,58] are used in thisembodiment for the delivery of pilot symbols as is described in thefollowing.

The transmission block 200 comprises a plurality of long preambles 202which are sent after the short preambles.

The signal values of the long preambles 202 that are transmitted in thefrequency subchannels of the indices [8,22,44,58] are given by thesignal values Λ_(f,t,n) wherein Λ_(f,t,n) denotes the signal value whichis transmitted in subchannel f via transmit antenna t at time n. Thesesignal values are also referred to as the pilots embedded in the longpreambles.

The receiver 102 receives via transmit antenna r and subchannel f attime n the discrete signal value (in the frequency domain)$\begin{matrix}{L_{f,r,n} = {{\left( {\sum\limits_{t = 1}^{N_{t}}\quad{H_{f,r,t}\Lambda_{f,t,n}}} \right){\mathbb{e}}^{j\quad 64\omega\quad n}} + V_{f,r,n}}} & (1)\end{matrix}$where H_(f,r,t) is the channel gain of the subchannel f establishedbetween transmit antenna t and receive antenna r, ω denotes the residualfrequency offset at the receiver 102 (as explained above afterperforming frequency offset estimation and frequency offset compensationbased on the short preambles 201) and V_(f,r,n) is the AWGN sample.

The time index n is chosen such that n=1 corresponds to the first of thelong preambles 201 and n=N_(LP) corresponds to the last of the longpreambles 201.

In the following, the selection of the Λ_(f,t,n) corresponding to fε[8,22, 44, 58] is explained. The L_(f,r,n) corresponding to these Λ_(f,t,n)according to equation (1) are used, after being processed by arespective FFT unit 108, by a residual frequency offset estimation unit109 to estimate the residual frequency offset ω.

It can be seen from (1) that if Λ_(f,t,n) is designed to be independentof t such that Λ_(f,t,n)=Λ_(f,t), ∀t=1, 2, . . . , N_(t), then thesignal $\begin{matrix}{\frac{L_{f,r,n}}{\Lambda_{f,n}} = {{\left( {\sum\limits_{t = 1}^{N_{t}}\quad H_{f,r,t}} \right){\mathbb{e}}^{j\quad 64\omega\quad n}} + \frac{V_{f,r,n}}{\Lambda_{f,n}}}} & (2)\end{matrix}$will sketch a complex sinusoid in n for every f and r when the noisesamples at different times n are shaped to the same variance by settingΛ_(f, t) = σ_(x)²which implies a fixed power in each pilot symbol.

Since fε[8, 22, 44, 58] and rε[1, 2, . . . , N_(r)], there exist 4N_(r)independent complex sinusoids of different amplitudes$\sum\limits_{t = 1}^{N_{t}}\quad H_{f,r,t}$but equal frequency 64ω.

To conform to the pilot values in IEEE802.11a (see [1]) as closely aspossible, the assignment

Λ_(8,n)=−Λ_(22,n)=Λ_(44,n)=Λ_(58,n)=1 is used in this embodiment.

A cyclic-prefix-free long preamble design is used in this embodiment. Inthis case, the last 16 of the 64 samples in each long preamble symbol inthe time domain need to be independent of n. This implies thatΛ_(f,n)=Λ_(f) for fε[8, 22, 44, 58]. The above criteria can besummarized as

C1) transmit antenna independence to produce independent complexsinusoids at the receiver 102

C2) subchannel pilot value assignment in consistence with IEEE802.11astandard

C3) time independence to satisfy requirement for cyclic-prefix-free longpreamble design

These criteria can be fulfilled by appointing $\begin{matrix}{\Lambda_{f,t,n} = \left\{ {\begin{matrix}{1,} & {{{if}\quad f} \in \quad\left\{ {8,44,58} \right\}} \\{{- 1},} & {{{if}\quad f} = 22}\end{matrix}.} \right.} & (3)\end{matrix}$

For N_(t)=6 and N_(t)=3, this is illustrated by table 1 for thesubchannels fε[8, 44, 58] and is illustrated by table 2 for thesubchannel f=22. TABLE 1 transmit antenna index time 1 1 1 1 1 1 index 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

TABLE 2 transmit antenna index time −1 −1 −1 −1 −1 −1 index −1 −1 −1 −1−1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1−1 −1

With (2), the problem of phase compensation is turned into one of thesingle tone parameter estimation, which is classical in the field ofsignal processing with a variety of ready solutions in the literature.The linear prediction estimator (see [2]) works to a reasonable accuracyat an affordable computational complexity and is particularly appealingin terms of implementation compared with Kay's estimator introduced in[2]. When applied to (2) for a single subchannel f and a single receiveantenna r, the estimator output reads $\begin{matrix}\begin{matrix}{\hat{\omega} = {\frac{1}{64}\angle{\sum\limits_{n = 2}^{N_{LP}}\quad{\left( \frac{L_{f,r,n}}{\Lambda_{f,n}} \right)\left( \frac{L_{f,r,{n - 1}}}{\Lambda_{f,{n - 1}}} \right)^{*}}}}} \\{= {\frac{1}{64}\angle{\sum\limits_{n = 2}^{N_{LP}}{L_{f,r,n}L_{f,r,{n - 1}}^{*}}}}}\end{matrix} & (4)\end{matrix}$

For N_(t)=6 and N_(r)=3 the L_(f,r,n) received by the receiver 102 areillustrated in tables 3 to 5 (where time grows downwards in the tables).TABLE 3 receive antenna 1 L_(8,1,1) L_(22,1,1) L_(44,1,1) L_(58,1,1)L_(8,1,2) L_(22,1,2) L_(44,1,2) L_(58,1,2) L_(8,1,3) L_(22,1,3)L_(44,1,3) L_(58,1,3) L_(8,1,4) L_(22,1,4) L_(44,1,4) L_(58,1,4)L_(8,1,5) L_(22,1,5) L_(44,1,5) L_(58,1,5) L_(8,1,6) L_(22,1,6)L_(44,1,6) L_(58,1,6)

TABLE 4 receive antenna 2 L_(8,2,1) L_(22,2,1) L_(44,2,1) L_(58,2,1)L_(8,2,2) L_(22,2,2) L_(44,2,2) L_(58,2,2) L_(8,2,3) L_(22,2,3)L_(44,2,3) L_(58,2,3) L_(8,2,4) L_(22,2,4) L_(44,2,4) L_(58,2,4)L_(8,2,5) L_(22,2,5) L_(44,2,5) L_(58,2,5) L_(8,2,6) L_(22,2,6)L_(44,2,6) L_(58,2,6)

TABLE 5 receive antenna 3 L_(8,3,1) L_(22,3,1) L_(44,3,1) L_(58,3,1)L_(8,3,2) L_(22,3,2) L_(44,3,2) L_(58,3,2) L_(8,3,3) L_(22,3,3)L_(44,3,3) L_(58,3,3) L_(8,3,4) L_(22,3,4) L_(44,3,4) L_(58,3,4)L_(8,3,5) L_(22,3,5) L_(44,3,5) L_(58,3,5) L_(8,3,6) L_(22,3,6)L_(44,3,6) L_(58,3,6)

On account of Λ_(f,t,n) being independent of t and n by design (asdescribed above), each column in tables 3 to 5 forms a complex sinusoidof a different amplitude but equal frequency. Using the received longpreambles, i.e. using the L_(f,r,n), the residual frequency offsetestimation unit 109 generates residual frequency offset estimates{circumflex over (ω)}_(LP,n) (depending on the current time given by thetime index n) according to $\begin{matrix}\begin{matrix}{{a_{{LP},1} = 0},} \\{a_{{LP},n} = {a_{{LP},{n - 1}} + {\sum\limits_{f \in {\lbrack{8,22,44,58}\rbrack}}\quad{\sum\limits_{r = 1}^{3}\quad{L_{f,r,n}L_{f,r,{n - 1},{n = 2},3,\cdots\quad,N_{LP}}^{*}}}}}} \\{{\hat{\omega}}_{{LP},n} = \frac{{\angle a}_{{LP},n}}{64}}\end{matrix} & (5)\end{matrix}$which is an extension of (4). The time index n=2 corresponds to thesecond long preamble of the long preambles 202, n=3 refers to the thirdlong preamble of the long preambles 202 and so on. Note that theresidual frequency offset estimate {circumflex over (ω)}_(LP,n) isdependent on time (note the time index n). When more L_(f,r,n) becomeavailable in the receiver 102 (corresponding to a growing time index n)the residual frequency offset estimate will typically become better.When all long preambles 202 have been transmitted, the residual FOE unit109 will have generated the residual frequency offset estimate{circumflex over (ω)}_(LP,N) _(LP) .

Finally, the transmission block 200 comprises a plurality of datasymbols 203 which are transmitted by the transmitter 101 after the longpreambles 202.

The signal values of the data symbols 203 that are transmitted in thefrequency subchannels of the indices [8, 22, 44, 58] are given by thesignal values Γ_(f,t,n) wherein Γ_(f,t,n) denotes the signal value whichis transmitted in subchannel f via transmit antenna t at time n. Thesesymbols are also referred to as the pilots embedded in the data symbols.

The pilots embedded in the data symbols can be developed followingsimilar principles as the pilots embedded in the long preambles. Incontrast to (1), the received signal values D_(f,r,n) corresponding tothe Γ_(f,t,n) are given by $\begin{matrix}{D_{f,r,n} = {{\left( {\sum\limits_{t = 1}^{N_{t}}\quad{H_{f,r,t}\Gamma_{f,t,n}}} \right){\mathbb{e}}^{j\quad 80\omega\quad n}} + {\overset{\sim}{V}}_{f,r,n}}} & (6)\end{matrix}$where as above, f specifies the subchannel, t the transmit antenna, rthe receive antenna and n is the time index.

To distinguish from V_(f,r,n), a different notation {tilde over(V)}_(f,r,n) is adopted for AWGN (additive white gaussian noise)samples. Unlike the long preambles Λ_(f,t,n) which can be manipulated sothat no cyclic-prefix is required, the data signal values Γ_(f,t,n)assume no such freedom. In the case of OFDM (orthogonal frequencydivision multiplexing), that is used in this embodiment, the presence ofcyclic prefix sets each OFDM symbol to 80 M-ary symbols in length.

Consequently, the frequency in (6) is 80ω) instead of 64ω) in (1) andcriteria C3 above is no longer applicable. The pilots are thus chosenindependent of t but dependent on f and n, or quantitatively$\begin{matrix}{\Gamma_{f,t,n} = \left\{ \begin{matrix}{k_{n},} & {{{if}\quad f} \in \quad\left\{ {8,44,58} \right\}} \\{{- k_{n}},} & {{{if}\quad f} = 22}\end{matrix} \right.} & (7)\end{matrix}$where k_(n)ε{1, −1} is a function of n in compliance with thepseudorandom sequence for the SISO pilots specified in the IEEE802.11astandard (see [1]).

The definition according to (7) is illustrated for N_(t)=6 and N_(r)=3,for the subchannels fε[8, 44, 58] in table 6 and is illustrated by table7 for the subchannel f=22. TABLE 6 transmit antenna index time k₁ k₁ k₁k₁ k₁ k₁ index k₂ k₂ k₂ k₂ k₂ k₂ k₃ k₃ k₃ k₃ k₃ k₃ . . . . . . . . . . .. . . . . . .

TABLE 7 transmit antenna index time −k₁ −k₁ −k₁ −k₁ −k₁ −k₁ index −k₂−k₂ −k₂ −k₂ −k₂ −k₂ −k₃ −k₃ −k₃ −k₃ −k₃ −k₃ . . . . . . . . . . . . . .. . . .

The pilots embedded in the data symbols, i.e. the D_(f,t,n) for fε[8,22, 44, 58] are used similarly as the pilots embedded in the longpreambles by the residual frequency offset estimation unit 109 toestimate the residual frequency offset.

The counter part of (4) in estimating each of the tone frequency in the4N_(r) subchannels is $\begin{matrix}\begin{matrix}{\hat{\omega} = {\frac{1}{80}\angle{\sum\limits_{n = 2}^{\infty}\quad{\left( \frac{D_{f,r,n}}{\Gamma_{f,n}} \right)\left( \frac{D_{f,r,{n - 1}}}{\Gamma_{f,{n - 1}}} \right)^{*}}}}} \\{= {\frac{1}{80}\angle{\sum\limits_{n = 2}^{\infty}{k_{n}k_{n - 1}D_{f,r,n}D_{f,r,{n - 1.}}^{*}}}}}\end{matrix} & (8)\end{matrix}$

Equation (8) is arrived at based on (7) and the property that k_(n)ε{1,−1} by design. By extending to multiple subchannels and rewriting inrecursive form, (8) becomes $\begin{matrix}{{{a_{{DATA},0} = {a_{{LP},N_{LP}}{\mathbb{e}}^{j\quad\frac{5}{4}\angle\quad a_{{LP},N_{LP}}}}},{k = 1}}{{D_{f,r,0} = L_{f,r,N_{LP}}},{a_{{DATA},n} = {a_{{DATA},{n - 1}} + {k_{n}k_{n - 1}{\sum\limits_{f \in {\lbrack{8,22,44,58}\rbrack}}{\sum\limits_{r = 1}^{3}{D_{f,r,n}D_{f,r,{n - 1}}^{*}}}}}}},{n = 1},2,\cdots\quad,{{\hat{\omega}}_{{DATA},n} = \frac{\angle\quad a_{{DATA},n}}{80}},}} & (9)\end{matrix}$

The accumulated sum a_(LP,N) _(LP) that is generated by the residual FOEunit 109 based on the long preambles according to (5) is used as thefirst value in a_(DATA,n) for accuracy enhancement. The exponentialfactor in the first line of (9) is introduced to account for thedifference in frequency arising from the absence of cyclic prefix in thelong preambles as indicated in (2) and (6).

In one embodiment, there may be two signal field symbols and n=1corresponds to the first signal field (SF) symbol, n=2 to the second SFsymbol, n=3 to the first data symbol and so on.

For N_(t)=6 and N_(r)=3 the D_(f,r,n) received by the receiver 102 areillustrated in tables 8 to 10 (where time grows downwards in thetables). TABLE 8 normalized receive antenna 1 values k₁D_(8,1,1)k₁D_(22,1,1) k₁D_(44,1,1) k₁D_(58,1,1) k₂D_(8,1,2) k₂D_(22,1,2)k₂D_(44,1,2) k₂D_(58,1,2) k₃D_(8,1,3) k₃D_(22,1,3) k₃D_(44,1,3)k₃D_(58,1,3) . . . . . . . . . . . .

TABLE 9 normalized receive antenna 2 values k₁D_(8,2,1) k₁D_(22,2,1)k₁D_(44,2,1) k₁D_(58,2,1) k₂D_(8,2,2) k₂D_(22,2,2) k₂D_(44,2,2)k₂D_(58,2,2) k₃D_(8,2,3) k₃D_(22,2,3) k₃D_(44,2,3) k₃D_(58,2,3) . . . .. . . . . . . .

TABLE 10 normalized receive antenna 3 values k₁D_(8,3,1) k₁D_(22,3,1)k₁D_(44,3,1) k₁D_(58,3,1) k₂D_(8,3,2) k₂D_(22,3,2) k₂D_(44,3,2)k₂D_(58,3,2) k₃D_(8,3,3) k₃D_(22,3,3) k₃D_(44,3,3) k₃D_(58,3,3) . . . .. . . . . . . .

Each of the columns in tables 8 to 10 can be regarded as a singlecomplex sinusoid.

In the following, the effect of a residual frequency offset in the timedomain on the symbols in the frequency domain is discussed. For ease ofpresentation, the noiseless case is considered, although the sameargument applies otherwise. Suppose a time sequence y_(n), n==1, 2, . .. , N, is multiplied with the complex sinusoid e^(j(ωn+φ)) where ω□1.Upon performing discrete Fourier transform on the product, the frequencydomain signal can be written in matrix form asy _(f)=FPy _(t)   (10)where y _(t)=[y₁ y₂ . . . y_(N)]^(T),

P=diag{e^(j(ω+φ)) e^(j(ω2+φ)) . . . e^(j(ωN+φ))} and F is the Fouriertransform matrix.

If the effect of the sinusoid is to be modelled in the frequency domainwith a diagonal matrix Q by $\begin{matrix}{{{\underset{\_}{y}}_{f} \approx {\underset{\_}{QFy}}_{t}}{then}} & (11) \\{\underset{\_}{Q} = {{{\underset{\_}{FPF}}^{H} \approx {\frac{\sum\limits_{k = 1}^{N}\quad{\mathbb{e}}^{j{({{\omega\quad k} + \phi})}}}{N}\underset{\_}{I}}} = {{{\mathbb{e}}^{j{({{\omega\frac{N + 1}{2}} + \phi})}}\left\lbrack \frac{\sin\left( \frac{\omega\quad N}{2} \right)}{N\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack}{\underset{\_}{I}.}}}} & (12)\end{matrix}$

The above approximation applies for the matrix F and any orthogonaltransform having fixed power in every element like the Hadamard matrix,and is exact at the diagonal entries. Based on such an approximation,the time domain models and frequency domain models are related asdepicted in table 11. TABLE 11 Time domain Freq domain CP0$\begin{bmatrix}{\mathbb{e}}^{j\omega} \\{\mathbb{e}}^{j\omega 2} \\\vdots \\{\mathbb{e}}^{j\omega 16}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{CP}\quad 0}$discarded LP1 $\begin{bmatrix}{\mathbb{e}}^{j\omega 17} \\{\mathbb{e}}^{j\omega 18} \\\vdots \\{\mathbb{e}}^{j\omega 80}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{CP}\quad 1}$$\begin{matrix}{\mathbb{e}}^{{{j\omega}\frac{80 + 17}{2}})} \\{\left\lbrack \frac{\sin\quad\left( {32\omega} \right)}{64\quad\sin\quad\left( \frac{\omega}{2} \right)} \right\rbrack{\underset{\_}{Fy}}_{{LP}\quad 1}}\end{matrix}\quad$ ⋮ ⋮ ⋮ LPN_(LP) $\begin{bmatrix}{\mathbb{e}}^{{j\omega}{\lbrack{{64{({N_{LP} - 1})}} + 17}\rbrack}} \\{\mathbb{e}}^{{j\omega}{\lbrack{{64{({N_{LP} - 1})}} + 18}\rbrack}} \\\vdots \\{\mathbb{e}}^{{j\omega}{\lbrack{{64{({N_{LP} - 1})}} + 80}\rbrack}}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{LP},N_{LP}}$$\begin{matrix}{\mathbb{e}}^{{j\omega}{\lbrack{{64{({N_{LP} - 1})}} + \frac{80 + 17}{2}}\rbrack}} \\{{{\left\lbrack \frac{\sin\quad\left( {32\omega} \right)}{64\quad\sin\quad\left( \frac{\omega}{2} \right)} \right\rbrack{\underset{\_}{Fy}}_{{LP},N_{LP}}}\quad}\quad}\end{matrix}\quad$ CP1 $\begin{bmatrix}{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 17})}} \\{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 18})}} \\\vdots \\{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 32})}}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{CP}\quad 1}$discarded Data 1 $\begin{bmatrix}{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 33})}} \\{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 34})}} \\\vdots \\{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + 96})}}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{DT}\quad 1}$$\begin{matrix}{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + \frac{96 + 33}{2}})}} \\{{{\left\lbrack \frac{\sin\quad\left( {32\omega} \right)}{64\quad\sin\quad\left( \frac{\omega}{2} \right)} \right\rbrack{\underset{\_}{Fy}}_{{DT}\quad 1}}\quad}\quad}\end{matrix}\quad$ ⋮ ⋮ ⋮ CP2 $\begin{bmatrix}{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 17}\rbrack}} \\{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 18}\rbrack}} \\\vdots \\{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 80}\rbrack}}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{CP}\quad 2}$discarded Data n $\begin{bmatrix}{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 33}\rbrack}} \\{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 34}\rbrack}} \\\vdots \\{\mathbb{e}}^{{j\omega}{\lbrack{{64N_{LP}} + {80{({n - 1})}} + 96}\rbrack}}\end{bmatrix}\quad\bullet\quad{\underset{\_}{y}}_{{DT}_{n}}$$\begin{matrix}{\mathbb{e}}^{{j\omega}{({{64N_{LP}} + {80{({n - 1})}} + \frac{96 + 33}{2}})}} \\{{{\left\lbrack \frac{\sin\quad\left( {32\omega} \right)}{64\quad\sin\quad\left( \frac{\omega}{2} \right)} \right\rbrack{\underset{\_}{Fy}}_{{DT}_{n}}}\quad}\quad}\end{matrix}\quad$ ⋮ ⋮ ⋮

While the N_(LP) long preambles share one single cyclic prefix of 16samples, the succeeding data symbols own a cyclic prefix each. As themodel shows, the discrete signals at receiver antenna r in the longpreamble and the data symbol segments are given respectively by$\begin{matrix}{\begin{matrix}{{{\mathbb{e}}^{{j64\omega}{({n - \frac{31}{128}})}}\left\lbrack \frac{\sin\left( {32\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack}{\underset{\_}{Fy}}_{{LP},n,}} & {{n = 1},2,\cdots\quad,N_{LP}}\end{matrix}{and}} & (13) \\\begin{matrix}{{{\mathbb{e}}^{{j80\omega}{({n + \frac{{128N_{LP}} - 31}{160}})}}\left\lbrack \frac{\sin\left( {32\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack}{\underset{\_}{Fy}}_{{DT},n,}} & {{n = 1},2,3,{\cdots\quad.}}\end{matrix} & (14)\end{matrix}$

As the received signal values are phase rotated in both the time andfrequency domains, the channel identified based on the distorted longpreambles can deviate considerably from the actual channel on account ofthe effect of residual frequency offset ω over a relatively longestimation interval in a MIMO system. In accordance with (13), theN_(LP) long preambles collected at subchannel f and receiver antenna rare related to the channel gain H_(f,r,t) and the transmitted valuesΛ_(f,t,n) by $\begin{matrix}{\quad\begin{matrix}{\begin{bmatrix}L_{f,r,1} \\L_{f,r,2} \\\vdots \\L_{f,r,N_{LP}}\end{bmatrix} = \left\lbrack \frac{\sin\left( {32\quad\omega} \right)}{64\quad{\sin\left( \frac{\omega}{\quad 2} \right)}} \right\rbrack} \\{\begin{bmatrix}{\mathbb{e}}^{j\quad 64{\omega{({1 - \frac{31}{128}})}}} & \quad & \quad & 0 \\\quad & {\quad{\mathbb{e}}^{{j64\omega}{({2 - \frac{31}{128}})}}} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\0 & \quad & \quad & {\quad{\mathbb{e}}^{{j64\omega}{({N_{LP} - \frac{31}{128}})}}}\end{bmatrix} \cdot} \\{\begin{bmatrix}\Lambda_{f,1,1} & \Lambda_{f,2,1} & \cdots & \Lambda_{f,N_{t},1} \\\Lambda_{f,1,2} & \Lambda_{f,2,2} & \cdots & \Lambda_{f,N_{t},2} \\\vdots & \vdots & ⋰ & \vdots \\\Lambda_{f,1,N_{LP}} & \Lambda_{f,2,N_{LP}} & \cdots & \Lambda_{f,N_{t},N_{LP}}\end{bmatrix}\begin{bmatrix}\begin{matrix}H_{f,r,1} \\H_{f,r,2}\end{matrix} \\\vdots \\H_{f,r,N_{t}}\end{bmatrix}}\end{matrix}} & (15)\end{matrix}$

In matrix form,${\underset{\_}{L}}_{f} = {\left\lbrack \frac{\sin\left( {32\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack{\underset{\_}{\overset{\_}{P}\quad\Lambda}}_{f}{\underset{\_}{h}}_{f,r}}$can be written. The conventional LS channel estimate with noconsideration of residual frequency offset is given by $\begin{matrix}\begin{matrix}{{\underset{\_}{\hat{h}}}_{f,r} = {\left( {{\underset{\_}{\Lambda}}_{f}^{H}{\underset{\_}{\Lambda}}_{f}} \right)^{- 1}{\underset{\_}{\Lambda}}_{f}^{H}{\underset{\_}{L}}_{f}}} \\{= {\left\lbrack \frac{\sin\left( {32\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack\left( {{\underset{\_}{\Lambda}}_{f}^{H}{\underset{\_}{\Lambda}}_{f}} \right)^{- 1}\left( {{\underset{\_}{\Lambda}}_{f}^{H}{\underset{\_}{\overset{\_}{P}\quad\Lambda}}_{f}} \right){\underset{\_}{h}}_{f,r}}} \\{\approx {{{{\mathbb{e}}^{{j64\omega}{({\frac{N_{LP} + 1}{2} - \frac{31}{128}})}}\left\lbrack \frac{\sin\left( {32\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack}\left\lbrack \frac{\sin\left( {32\omega\quad N_{LP}} \right)}{N_{LP}\quad{\sin\left( {32\omega} \right)}} \right\rbrack}{\underset{\_}{h}}_{f,r}}}\end{matrix} & (16)\end{matrix}$upon using the property in (12) and assuming that Λ=constant×F (orinstead of the Fourier transform any orthogonal transform with equalpower in every element like the Hadamard transform) which is reasonablyvalid for optimal long preamble design. By (14), the data symbolsreceived at subchannel f and antenna r at time n for a MIMO-OFDM systemadopting, for instance, a VBLAST (Vertical Bell-Lab Layered Space-Time)structure, is $\begin{matrix}\begin{matrix}{\begin{bmatrix}Y_{f,1,n} \\Y_{f,2,n} \\\vdots \\Y_{f,N_{r},n}\end{bmatrix} = {{\mathbb{e}}^{{j80\omega}{({n + \frac{{128N_{LP}} - 31}{160}})}}\left\lbrack \frac{\sin\left( {32\quad\omega} \right)}{64\quad{\sin\left( \frac{\omega}{2} \right)}} \right\rbrack}} \\{\begin{bmatrix}H_{f,1,1} & H_{f,1,2} & \cdots & H_{f,1,N_{t}} \\H_{f,2,1} & H_{f,2,2} & \cdots & H_{f,2,N_{t}} \\\vdots & \vdots & ⋰ & \vdots \\H_{f,N_{r},1} & H_{f,N_{r},2} & \cdots & H_{f,N_{r},N_{t}}\end{bmatrix}\begin{bmatrix}X_{f,1,n} \\X_{f,2,n} \\\vdots \\X_{f,N_{t},n}\end{bmatrix}} \\{= \frac{{\mathbb{e}}^{{j\omega}{\lbrack{{80{({n + \frac{{128N_{LP}} - 31}{160}})}} - {64{({\frac{N_{LP} + 1}{2} - \frac{31}{128}})}}}\rbrack}}}{\left\lbrack \frac{\sin\left( {32\omega\quad N_{LP}} \right)}{N_{LP}\quad{\sin\left( {32\omega} \right)}} \right\rbrack}} \\{\begin{bmatrix}{\hat{H}}_{f,1,1} & {\hat{H}}_{f,1,2} & \cdots & {\hat{H}}_{f,1,N_{t}} \\{\hat{H}}_{f,2,1} & {\hat{H}}_{f,2,2} & \cdots & {\hat{H}}_{f,2,N_{t}} \\\vdots & \vdots & ⋰ & \vdots \\{\hat{H}}_{f,N_{r},1} & {\hat{H}}_{f,N_{r},2} & \cdots & {\hat{H}}_{f,N_{r},N_{t}}\end{bmatrix}\begin{bmatrix}X_{f,1,n} \\X_{f,2,n} \\\vdots \\X_{f,N_{t},n}\end{bmatrix}}\end{matrix} & (17)\end{matrix}$after making use of (16), implying $\begin{matrix}\begin{matrix}{\begin{bmatrix}X_{f,1,n} \\X_{f,2,n} \\\vdots \\X_{f,N_{t},n}\end{bmatrix} = {\begin{bmatrix}{\hat{H}}_{f,1,1} & {\hat{H}}_{f,1,2} & \cdots & {\hat{H}}_{f,1,N_{t}} \\{\hat{H}}_{f,2,1} & {\hat{H}}_{f,2,2} & \cdots & {\hat{H}}_{f,2,N_{t}} \\\vdots & \vdots & ⋰ & \vdots \\{\hat{H}}_{f,N_{r},1} & {\hat{H}}_{f,N_{r},2} & \cdots & {\hat{H}}_{f,N_{r},N_{t}}\end{bmatrix}^{- 1} \cdot}} \\{\left( {\frac{\sin\left( {32\omega\quad N_{LP}} \right)}{N_{LP}{\sin\left( {32\omega} \right)}}{{\mathbb{e}}^{- {{j80\omega}{\lbrack{n + \frac{2{({N_{LP} - 1})}}{5}}\rbrack}}}\begin{bmatrix}Y_{f,1,n} \\Y_{f,2,n} \\\vdots \\Y_{f,N_{r},n}\end{bmatrix}}} \right).}\end{matrix} & (18)\end{matrix}$

While the amplitude attenuation$\frac{\sin\left( {32\omega\quad N_{LP}} \right)}{N_{LP}\quad{\sin\left( {32\omega} \right)}}$is time-invariant and negligible due to a small ω after frequency offsetestimation and compensation based on the short preambles, the phaserotation term is an increasing function of time and is thusindispensable. Therefore to provide the amount of phase compensation forthe distortion in both the channel estimate and the data symbols, thereceived signal values Y_(f,r,n) are replaced by a residual frequencyoffset compensation unit 110 by $\begin{matrix}{{{{\hat{Y}}_{f,r,n} = {Y_{f,r,n}{\mathbb{e}}^{{- {j{\lbrack{n + \frac{2{({N_{LP} - 1})}}{5}}\rbrack}}}\angle\quad a_{{DATA},{n - 1}}}}},{n = 1},2,\cdots\quad,{f = 1},2,3,\cdots\quad,64,{and}}{f \neq \left\{ {8,22,44,58} \right\}}} & (19)\end{matrix}$

After this, the signal values corrected in this way are supplied to azero forcing interference suppression (ZFIS) unit 111 which serves alsoas a channel equalizer (and for data detection). The output of the ZFISunit 111 is supplied to a decoder 112 which performs the decoding of thedata.

Although the above development is derived for the VBLAST configuration,it is straightforward to show that the same compensation formula in (19)holds for a GSTBC (Groupwise Space-Time Block Code) system. It is alsoremarked that for the case when the long preambles are loaded withcyclic prefix, the same phase compensation can be readily applied toarrive at the equations $\begin{matrix}{{Long}\quad{preambles}\text{:}} & \quad \\\begin{matrix}{{a_{{LP},1} = 0},} \\{a_{{LP},n} = {a_{{LP},{n - 1}} +}} \\{{\sum\limits_{f \in {\lbrack{8,22,44,58}\rbrack}}\quad{\sum\limits_{r = 1}^{3}\quad{L_{f,r,n}L_{f,r,{n - 1}}^{*}}}},{n = 2},3,\cdots\quad,N_{LP}} \\{{\hat{\omega}}_{{LP},n} = {\frac{\angle\quad a_{{LP},n}}{80}.}}\end{matrix} & (20) \\{{Data}\quad{symbols}\text{:}} & \quad \\\begin{matrix}{{a_{{DATA},0} = a_{{LP},N_{LP}}},} \\{{k_{0} = 1},} \\{{D_{f,r,0} = L_{f,r,N_{LP}}},} \\{a_{{DATA},n} = {a_{{DATA},{n - 1}} +}} \\{k_{n}k_{n - 1}{\sum\limits_{f \in {\lbrack{8,22,44,58}\rbrack}}\quad{\sum\limits_{r = 1}^{3}\quad{D_{f,r,n}D_{{f,r,{n - 1},}\quad}^{*}}}}} \\{{n = 1},2,\cdots\quad,} \\{{\hat{\omega}}_{{DATA},n} = \frac{\angle\quad a_{{DATA},n}}{80}}\end{matrix} & (21) \\{{Phase}\quad{compensation}\text{:}} & \quad \\\begin{matrix}{{{\hat{Y}}_{f,r,n} = {Y_{f,r,n}{\mathbb{e}}^{{- {j{\lbrack{n + \frac{({N_{LP} - 1})}{2}}\rbrack}}}\angle\quad a_{{DATA},{n - 1}}}}},} \\{{n = 1},2,\cdots\quad,} \\{{f = 1},2,3,\cdots\quad,64,{{{and}\quad f} \neq \left\{ {8,22,44,58} \right\}}}\end{matrix} & (22)\end{matrix}$that yield identical performance using the pilot designs according to(3) and (7) since the difference lies only in a less efficient use oflong preambles in communicating information.

In the embodiment described above, no channel estimation is required ofthe pilot subchannels. Instead, a_(LP,n) is computed after each longpreamble is received in accordance with (5).

Upon arrival of every OFDM symbol, a_(DATA,n) is updated as specified in(9). Phase compensation on Y_(f,r,n) is carried out to obtain Ŷf,r,m in(19) for subsequent processing such as channel equalization, etc.

Simulation results show that the method provides almost perfectcompensation. Simplicity in implementation is obvious as only a fewinevitable non-linear operations are required by design.

In case of a MIMO OFDM system, in each long training preamble, signalfield and OFDM symbol, eight of the subcarriers are in one embodimentdedicated to pilot signals in order to make the coherent detectionrobust against frequency offset and phase noise. These pilot signalsshall be put in subcarriers −48, −34, −20, −6, 6, 20, 34, and 48. Thepilots in the long training preamble are not modulated over time butthose in the signal field and the OFDM data symbols shall be BPSKmodulated by a pseudo binary sequence to prevent the generation ofspectral lines. The contribution of the pilot subcarriers to each OFDMsymbol is described in in the following.

The contribution of the pilot subcarriers for the n^(th) OFDM symbol isproduced by Fourier transform of sequence P_(−58,58) or P_(−53,53) givenbelow.

First, define the sequence

P_(−26,26)={0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,−1,0,0,0,0,0}.

then

P_(−53,53)={P_(−26,26), 0, P_(−26,26)}.

P_(−58,58)={P_(−26,26), 0,0,0,0,0,0,0,0,0,0,0, P_(−26,26)}.

The polarity of the pilot subcarriers is controlled by the sequence,p_(n), which is a cyclic extension of the 127 elements sequence and isgiven by

P_(0 . . . 126)={1,1,1,1, −1,−1,−1,1, −1,−1,−1,−1, 1,1,−1,1, 1,1,1,1,1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,−1,1, 1,−1,−1,1, 1,1,−1,1, −1,−1,−1,1,−1,1−1,1, 1,−1,−1,1, 1,1,1,1, −1,−1,1,1, −1,−1,1,−1, 1,−1,1,1,−1,−1,−1,1, 1,−1,−1,−1, −1,1,−1,−1, 1,−1,1,1, −1,−1,−1,−1, −1,1,−1}

Each sequence element is used for one OFDM symbol. The first and secondelements, p₀ and p₁, multiply the pilot subcarriers of the first andsecond SIGNAL symbol, respectively, while the elements from p₂ on areused for the DATA symbols.

In this document, the following publications are cited:

-   [1] “Part 11: wireless LAN medium access control (MAC) and physical    layer (PHY) specifications: High-speed physical layer in the 5 GHz    band.” IEEE std 802.11a—1999: Supplement to IEEE 802.11-1999,    September 1996-   [2] S. Kay, “Statistically/Computationally efficient frequency    estimation”, ICASSP'98, pp. 2292-2294, vol. 4, 1998

1. A method for determining a residual frequency offset between atransmitter and a receiver in a transmission of data via a communicationchannel, wherein: a message is transmitted from the transmitter to thereceiver via the communication channel; the message comprises at leastone short preamble, at least one long preamble and user data; the atleast one long preamble comprises residual frequency offsetdetermination information; and the residual frequency offset isdetermined based on the residual frequency offset determinationinformation.
 2. A method according to claim 1, wherein the at least oneshort preamble comprises frequency offset determination information anda frequency offset is determined based on the frequency offsetdetermination information.
 3. A method according to claim 1, wherein thedata comprises further residual frequency offset determinationinformation and a residual frequency offset determination is carried outbased on the further residual frequency offset determinationinformation.
 4. A method according to claim 1 wherein the communicationchannel comprises at least one data subchannel and at least one pilotsubchannel.
 5. A method according to claim 4, wherein the at least onelong preamble further comprises channel estimation information based onwhich a channel estimation is performed to determine the transmissioncharacteristics of the communication channel and the residual frequencyoffset determination information is transmitted via the at least onepilot subchannel and the channel estimation information is transmittedvia the at least one data subchannel.
 6. A method according to claim 1,wherein the message is transmitted via a plurality of transmit antennas.7. A method according to claim 1, wherein the message is received via aplurality of receive antennas.
 8. A method according to claim 1, whereinthe message is transmitted according to OFDM.
 9. A method according toclaim 1, wherein, when the residual frequency offset has been determinedbased on the residual frequency offset determination information, aphase compensation is carried out for at least one signal value which isreceived in the transmission of the message based on the determinedresidual frequency offset.
 10. A communication system comprising atransmitter and a receiver wherein: the transmitter is adapted totransmit a message from the transmitter to the receiver via acommunication channel wherein the message comprises at least one shortpreamble, at least one long preamble and user data and the at least onelong preamble comprises residual frequency offset determinationinformation; and the receiver is adapted to determine a residualfrequency offset between the transmitter and the receiver in thetransmission of data via the communication channel based on the residualfrequency offset determination information.
 11. A method fortransmitting a message by a transmitter, wherein: a message is generatedwherein the message comprises at least one short preamble, at least onelong preamble and user data and the at least one long preamble comprisesresidual frequency offset determination information; and the message istransmitted to a receiver via a communication channel; wherein theresidual frequency offset determination information allows the receiverto determine a residual frequency offset between the transmitter and thereceiver in the transmission of data via the communication channel. 12.A transmitter comprising: a message generating unit adapted to generatea message wherein the message comprises at least one short preamble, atleast one long preamble and user data and the at least one long preamblecomprises residual frequency offset determination information; a sendingunit adapted to transmit the message to a receiver via a communicationchannel; wherein the residual frequency offset determination informationallows the receiver to determine a residual frequency offset between thetransmitter and the receiver in the transmission of data via thecommunication channel.
 13. A method for processing a message by areceiver wherein: a message is received from a transmitter via acommunication channel which message comprises at least one shortpreamble, at least one long preamble and user data, wherein the at leastone long preamble comprises residual frequency offset determinationinformation; and a residual frequency offset between the transmitter andthe receiver in a transmission of data via the communication channel isdetermined based on the residual frequency offset determinationinformation.
 14. A receiver comprising: a receiving unit adapted toreceive a message from a transmitter via a communication channel whichmessage comprises at least one short preamble, at least one longpreamble and user data, wherein the at least one long preamble comprisesresidual frequency offset determination information; and a determiningunit adapted to determine a residual frequency offset between thetransmitter and the receiver in a transmission of data based on theresidual frequency offset determination information.